Acceptable limits of degradation of TBC for high-efficient turbines (HET TBC) Department Materials (ALSTOM) Lab of Crystallography (ETH Zürich) CTI project Nr EPRP-IW Project startNov Project duration24 months

High temperature thermal conductivity of granular structures

Recent theory of TC of PS YSZ coatings and its comparison with experiments Z. Wang, A. Kulkarni, S. Deshpande, T. Nakamura, H. Herman, Acta Materialia 51, 5319 (2003) The theory takes into account everything (cracks, pores, and voids) except the phonon scattering at the splat boundaries

Phonon transport in the granular material. The model Assumptions: The size of grains much exceeds the distance between them Scattering by the inter-grain boundaries is the main mechanism restricting TC The mean spacing between the localized phonon levels is small enough. This is the case of large grains Energies of these levels are distributed on the interval [0,  D ] according to the Debye law

20 µm 200 µm

Conductivity of the 3D lattice of random resistors

Temperature dependence of TC

Only the phonon scattering at the grain boundaries has been taken into account Debye temperature is TD=1042K for Al2O3 and TD=963K for YSZ. Thus, TC is constant for T>700C

Factor of disorder in the iterlamellar contacts Conductivities are assumed to be distributed on the interval [1-  /2, 1+  /2], i.e.,  2 =  2 /12

Effect of porosity in Al 2 O 3 Small size pores: Large size pores: factor Very large porosity: factor

Phonon-phonon interaction

Measurements

Modeling t=0.069t=0.073 t=0.066 t=0.028 t=0.038t=0.030

Parameters necessary for HEATNANO Physical data of the Material Lattice constants Debye temperature Dielectric permittivity Thermal conductivity as a function of temperature of the bulk material Parameters of the structure Average grain size (d) or lamal size ? SEM, XRD Diameter of the contact area (S) with e.s.d. SEM * Coordination number (Z) SEM * Thickness of the film SEM Porosity SEM * The value of Z·S can be expressed via the interlamal porosity

Adaptation of HEATNANO to PS YSZ Problem of multi-phase granular material. The model should include different type of randomly distributed resistors associated with different t values Problem of lamellar anisotropy. In-plane and cross-plane phonon hopping can be characterized with the same t value; however the values of and Z should be different Porosity that is characteristic for YSZ. The small-size porosity like that considered by Z. Wang et al. [Acta Materialia 51, 5319 (2003)] will be introduced in The large-size porosity will be considered like it has been done in our model [Phys. Rev. B 70, art. no (2004) ] Start of the first version of HEATNANO for PS YSZ is the middle of January 2006